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MathNet 2025-part-01 — 187 problems (EN–VI) Question 152

Math Olympiad Vault · MathNet 2025-part-01 — 187 problems (EN–VI)

Question 152

A country consists of $n$ islands. Some pairs of islands are connected by bridges. For any two islands that are connected via some sequence of bridges, the *distance* between them is defined as the minimum number of bridges that must be crossed to travel from one island to the other.
Assume that each island is directly connected by bridges to at least $m$ other islands. What is the maximum possible distance between two islands?